Abstract: | Let be a connected graph with edges. An antimagic labeling of is a one-to-one mapping from to such that the vertex sum (i.e., sum of the labels assigned to edges incident to a vertex) for distinct vertices are different. A graph is called antimagic if has an antimagic labeling. It was conjectured by Hartsfield and Ringel that every tree other than is antimagic. The conjecture remains open though it was verified for trees with some constrains. Caterpillars are an important subclass of trees. This paper shows caterpillars with maximum degree 3 are antimagic, which gives an affirmative answer to an open problem of Lozano et al. (2019). |